Optimal cascaded control of mobile manipulators

In this study, the solution to the kinematically optimal control problem of the mobile manipulators is proposed. Both dynamic equations are assumed to be uncertain, and globally unbounded disturbances are allowed to act on the mobile manipulator when tracking the trajectory by the end effector. We propose a computationally efficient class of cascaded control algorithms, which are based on an extended Jacobian transpose matrix. Our controllers involve two new non-singular terminal sliding mode manifolds defined by nonlinear integral equalities of both the second order with respect to the task space tracking error and the first order with respect to reduced mobile manipulator acceleration. Using the Lyapunov stability theory, we prove that the proposed Jacobian transpose cascaded control schemes are finite time stable provided that some practically reasonable assumptions are fulfilled during the mobile manipulator movement. The numerical examples carried out for mobile manipulators [consisting of a non-holonomic platform of type (2, 0) and holonomic manipulators of 2 and 3 revolute kinematic pairs], which operate in two-dimensional and three-dimensional work spaces, respectively, illustrate both the trajectory tracking performance of the proposed control schemes and simultaneously their minimising property for some practically useful objective function.